Question

Complete the statements about the system's possible solutions.

The point (4,6) is ___ of this system.
The point (6,5) is ___ of this system.

Answer 1

The point (4,6) is a possible solution of the system, and the point (6,5) is not a solution of the system.

Step-by-step explanation:

The point (4,6) is a possible solution of this system, and the point (6,5) is not a solution of this system.

In order to determine if a point is a solution of a system of equations, we substitute the values of the coordinates into the equations and check if they satisfy the equations.

For example, if we have a system of equations:

Equation 1: 2x + y = 10

Equation 2: 3x - y = 4

We substitute the coordinates (4,6) into the equations:

Equation 1: 2(4) + 6 = 10

16 + 6 = 10

Equation 2: 3(4) - 6 = 4

12 - 6 = 4

Both equations are true, so (4,6) is a solution of the system.

Similarly, we substitute the coordinates (6,5) into the equations:

Equation 1: 2(6) + 5 = 10

12 + 5 = 10

Equation 2: 3(6) - 5 = 4

18 - 5 = 4

One or both equations are false, so (6,5) is not a solution of the system.